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A new design of an optical isolator based on photonic transitions in the interbands of a honeycomb structure that generates a dual negative refraction in a photonic crystal is presented. The involved photonic transition is associated to the perturbation of the dielectric constant of the medium. The band structure is determined using the plane wave method where the transmission spectra, field profile, and mode amplitudes are obtained by applying the finite difference time domain method. Due to the time-dependent perturbation of the refractive index of the medium that constitutes the dual negative refraction, asymmetric transmission mechanism is achieved for one of the desired modes, demonstrating optical isolation. Using the dual negative refraction effect in photonic crystal structure, the optical isolation is reported for only one of the desired optical modes. It is anticipated that the proposed mode conversion mechanism can be employed for designing ultrahigh-speed optical interconnections. The proposed optical isolator model is expected to have a significant impact on designing ultrahigh-speed integrated optical platforms.